Start Date

November 2016

End Date

November 2016

Location

HUB 302-159

Type of Presentation

Poster

Abstract

The spread of infectious diseases is a complex process influenced by evolutionary behavior as well as ecological, demographic, and socioeconomic conditions. Researchers have described infections’ interactions through mathematical models, such as the Susceptible-Infected-Recovered/Removed (SIR) model. The SIR model uses compartmentalizing techniques to explain the interaction between groups through differential equations. However, the SIR model, characterized by its simplicity, grazes over the unique behaviors diseases exhibit. This work aims to expand and generalize the SIR model by using different equations to mathematically interpret subpopulations’ interactions. Our equations include the three principles of evolution­­– replication, mutation, and selection– allowing for an analysis of disease transmission through an evolutionary perspective. Due to its incorporation of evolutionary principles, we refer to our model as the SRM model. Through MATLAB, we produce simulations to analyze diseases’ presence in the population by noting the subpopulations’ behavior overtime. Lastly, by using linear stability analysis we identify points of equilibrium, particularly fixed points, that allow us to analyze the tendencies of population change. Ultimately, by utilizing general equations we aim to generate a robust model that can capture the complexities of disease transmission.

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Nov 12th, 1:00 PMNov 12th, 2:00 PM

Dynamic Modeling of Diseases: Measles

HUB 302-159

The spread of infectious diseases is a complex process influenced by evolutionary behavior as well as ecological, demographic, and socioeconomic conditions. Researchers have described infections’ interactions through mathematical models, such as the Susceptible-Infected-Recovered/Removed (SIR) model. The SIR model uses compartmentalizing techniques to explain the interaction between groups through differential equations. However, the SIR model, characterized by its simplicity, grazes over the unique behaviors diseases exhibit. This work aims to expand and generalize the SIR model by using different equations to mathematically interpret subpopulations’ interactions. Our equations include the three principles of evolution­­– replication, mutation, and selection– allowing for an analysis of disease transmission through an evolutionary perspective. Due to its incorporation of evolutionary principles, we refer to our model as the SRM model. Through MATLAB, we produce simulations to analyze diseases’ presence in the population by noting the subpopulations’ behavior overtime. Lastly, by using linear stability analysis we identify points of equilibrium, particularly fixed points, that allow us to analyze the tendencies of population change. Ultimately, by utilizing general equations we aim to generate a robust model that can capture the complexities of disease transmission.